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Simple Quadratic Problem

  1. Oct 17, 2007 #1
    1. The problem statement, all variables and given/known data
    I am trying to use the quadratic formula for 3x^2 - 12x +11 and I am getting...
    12 +/- (sqrt 12)/6 which is supposed to reduce to 6 +/- (sqrt 3)/3 and I can't figure it out...it's very sad!!!
     
  2. jcsd
  3. Oct 17, 2007 #2

    rock.freak667

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    [tex]\sqrt{12} = \sqrt{4*3}= \sqrt{4}\sqrt{3} =2\sqrt{3}[/tex]
     
  4. Oct 17, 2007 #3

    symbolipoint

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    The 2/2 cancels, involving the distributive property.

    You did not use grouping symbols correctly in your message, but see the steps:

    ((2*2*3) +/- (2*2*3)^(.5))/(2*3)
    =((2*2*3) +/- (2)*(3^(0.5)))/(2*3)
    = 2*(2*3 +/- (3^(0.5)))/(2*3)
    Notice the factor of 2 in numerator and factor of 2 in denominator; you need to write these steps longhand so you can see clearly; no typesetting system here on my end...
    ... simplifies quite well to
    =(2*3 +/- (3^(0.5)))/3
    =(6 +/- (3^(0.5))/3

    Also watch my work carefully in case I make any grouping symbol error. I just caught a few that I corrected, but again check carefully.
     
  5. Oct 18, 2007 #4
    So you have (12 * 2 * sqrt 3) / 6 which simplifies to (6 * 1 * sqrt3) / 3 then to
    (6 * sqrt 3) / 3
     
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